Linear Operators, Part 2 |
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Page 1241
then , letting zn = Xn - Yn , we have limn _ n = 0 and limm . n - 7002m - 2n + = 0 .
Consequently there is a number M such that 12m1 + SM , m = 1 , 2 , . . . .
Moreover , given a > 0 there is an integer N such that if m , n > N , then 12m — %
1 + < ε .
then , letting zn = Xn - Yn , we have limn _ n = 0 and limm . n - 7002m - 2n + = 0 .
Consequently there is a number M such that 12m1 + SM , m = 1 , 2 , . . . .
Moreover , given a > 0 there is an integer N such that if m , n > N , then 12m — %
1 + < ε .
Page 1383
With boundary conditions A , the eigenvalues are consequently to be determined
from the equation sin vă = 0 . Consequently , in Case A , the eigenvalues 2 are
the numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } ? , n 2
...
With boundary conditions A , the eigenvalues are consequently to be determined
from the equation sin vă = 0 . Consequently , in Case A , the eigenvalues 2 are
the numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } ? , n 2
...
Page 1387
If Il > 0 , the linear combination eivāt = cos Vat + i sin Vat belongs to L2 ( 0 , 0 ) ; if
In < 0 , the linear combination p - ivāt = cos Vīt - i sin Vīt belongs to L , ( 0 , 0 ) .
Consequently , by Theorem 3 . 16 , the resolvent R ( 2 ; T ) is an integral operator
...
If Il > 0 , the linear combination eivāt = cos Vat + i sin Vat belongs to L2 ( 0 , 0 ) ; if
In < 0 , the linear combination p - ivāt = cos Vīt - i sin Vīt belongs to L , ( 0 , 0 ) .
Consequently , by Theorem 3 . 16 , the resolvent R ( 2 ; T ) is an integral operator
...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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